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From Amie I first heard about Yitang Zhang, a solitary, part-time calculus teacher at the University of New Hampshire who received several prizes, including a MacArthur award in September, for solving a problem that had been open for more than a hundred and fifty years. The problem that Zhang chose, in 2010, is from number theory, a branch of pure mathematics. Pure mathematics, as opposed to applied mathematics, is done with no practical purposes in mind. It is as close to art and philosophy as it is to engineering. “My result is useless for industry,” Zhang said. The British mathematician G. H. Hardy wrote in 1940 that mathematics is, of “all the arts and sciences, the most austere and the most remote.” Bertrand Russell called it a refuge from “the dreary exile of the actual world.” Hardy believed emphatically in the precise aesthetics of math. A mathematical proof, such as Zhang produced, “should resemble a simple and clear-cut constellation,” he wrote, “not a scattered cluster in the Milky Way.” Edward Frenkel, a math professor at the University of California, Berkeley, says Zhang’s proof has “a renaissance beauty,” meaning that though it is deeply complex, its outlines are easily apprehended. The pursuit of beauty in pure mathematics is a tenet. Last year, neuroscientists in Great Britain discovered that the same part of the brain that is activated by art and music was activated in the brains of mathematicians when they looked at math they regarded as beautiful.

When someone refers to a Hispanic person or a lesbian or someone with blue eyes or curly hair or double-jointed thumbs, it’s not unreasonable to question whether the detail is merely a rhetorical flourish of sorts or is, in the speaker’s mind, substantively relevant. Such superfluous details can often be offered as a way of reinforcing a stereotype without outright stating it. It is no surprise that we often respond to statements like “My black coworker is always late” or “That blonde student is actually quite smart” or “My gay friend is so dramatic” by asking what, exactly, the speaker is “trying to say.” We are entitled to our indignation because the language presented a very clear alternative; these traits needn’t have been mentioned at all.

When it comes to gender, on the other hand, the language has traditionally presented no elegant alternative. We are forced to clumsily dance around the matter, or to give in and refer to our coworkers, students and friends as “he” or “she.”

Instead, we ought to revert to the gender neutral “they” whenever gender is not explicitly relevant. Least of all because, if the goal is greater inclusion, limiting the use of the singular they to these cases doesn’t even have the desired effect.

How large is Africa compared to the United States, or Western Europe? Most inhabitants of the latter places might guess it is a little larger, but few would have any idea of the scale of the difference. This has led German graphics designer Kai Krause to produce this map to shake people's perceptions a little.

Any attempt to map a spherical planet onto a flat map will involve distortions of size, shape or both. There is a passionate debate among cartographers about the best way to hang the world on a wall, but most agree that the most common maps we get our sense of the world from are very bad ways to do it. The problem is that these maps exaggerate the size of the countries at high  latitudes, and shrink places near the equator - leading to a perception that Europe is larger than South America, to pick just one example among many.

Africa, which spans the equator, fares particularly badly on these sorts of projections: Krause says, "Africa is so mind-numbingly immense, that it exceeds the common assumptions by just about anyone I ever met: it contains the entirety of the USA, all of China, India, as well as Japan and pretty much all of Europe as well - all combined!”  Some have argued that since people associate size with importance this encourages the already strong tendency of the world's wealthiest nations to disregard those who live in the tropics. 

If we’re going to rely on science as a means for reaching the truth — and it’s still the best tool we have — it’s important that we understand and respect just how difficult it is to get a rigorous result

Scientists’ overreliance on p-values has led at least one journal to decide it has had enough of them. In February, Basic and Applied Social Psychology announced that it will no longer publish p-values.

P-hacking and similar types of manipulations often arise from human biases. “You can do it in unconscious ways — I’ve done it in unconscious ways,” Simonsohn said. “You really believe your hypothesis and you get the data and there’s ambiguity about how to analyze it.” When the first analysis you try doesn’t spit out the result you want, you keep trying until you find one that does.

Clinical research can never prove that an intervention has an effect size of zero. Rather, clinical research assumes the null hypothesis, that the treatment does not work, and the burden of proof lies with demonstrating adequate evidence to reject the null hypothesis. So, when being technical, researchers will conclude that a negative study “fails to reject the null hypothesis.” Further, negative studies do not demonstrate an effect size of zero, but rather that any possible effect is likely to be smaller than the power of existing research to detect. The greater the number and power of such studies, however, the closer this remaining possible effect size gets to zero. At some point the remaining possible effect becomes clinically insignificant. In other words, clinical research may not be able to detect the difference between zero effect and a tiny effect, but at some point it becomes irrelevant. What David and I have convincingly argued, in my opinion, is that after decades of research and more than 3000 trials, acupuncture researchers have failed to reject the null hypothesis, and any remaining possible specific effect from acupuncture is so tiny as to be clinically insignificant.

It is clear from meta-analyses that results of acupuncture trials are variable and inconsistent, even for single conditions. After thousands of trials of acupuncture and hundreds of systematic reviews,18 arguments continue unabated. In 2011,Pain published an editorial31 that summed up the present situation well. “Is there really any need for more studies? Ernst et al.18 point out that the positive studies conclude that acupuncture relieves pain in some conditions but not in other very similar conditions. What would you think if a new pain pill was shown to relieve musculoskeletal pain in the arms but not in the legs? The most parsimonious explanation is that the positive studies are false positives. In his seminal article on why most published research findings are false, Ioannidis32 points out that when a popular but ineffective treatment is studied, false positive results are common for multiple reasons, including bias and low prior probability.” Since it has proved impossible to find consistent evidence after more than 3000 trials, it is time to give up. It seems very unlikely that the money that it would cost to do another 3000 trials would be well-spent.

How did we come to care so much about creativity? The language surrounding it, of unleashing, unlocking, awakening, developing, flowing, and so on, makes it sound like an organic and primordial part of ourselves which we must set free—something with which it’s natural to be preoccupied. But it wasn’t always so; people didn’t always care so much about, or even think in terms of, creativity.

It was Romanticism, in the late eighteenth and early nineteenth centuries, which took the imagination and elevated it, giving us the “creative imagination.”

How did creativity transform from a way of being to a way of doing? The answer, essentially, is that it became a scientific subject, rather than a philosophical one.

Empathy research is thriving these days, as cognitive neuroscience undergoes what some call an “affective revolution.” There is increasing focus on the emotions, especially those involved in moral thought and action. We’ve learned, for instance, that some of the same neural systems that are active when we are in pain become engaged when we observe the suffering of others. Other researchers are exploring how empathy emerges in chimpanzee and other primates, how it flowers in young children, and the sort of circumstances that trigger it.

Rifkin calls for us to make the leap to “global empathic consciousness.” He sees this as the last best hope for saving the world from environmental destruction, and concludes with the plaintive question “Can we reach biosphere consciousness and global empathy in time to avoid planetary collapse?”

This enthusiasm may be misplaced, however. Empathy has some unfortunate features—it is parochial, narrow-minded, and innumerate. We’re often at our best when we’re smart enough not to rely on it.